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Volume 18, Issue 3
A Family of High-Order Parallel Rootfinders for Polynomials

Shi-Ming Zheng

J. Comp. Math., 18 (2000), pp. 283-288.

Published online: 2000-06

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  • Abstract

In this paper we present a family of parallel iterations of order $m+2$ with parameter $m=0,1,...$ for simultaneous finding all zeros of a polynomial without evaluation of derivatives, which includes the well known Weierstrass-Durand-Dochev-Kerner and Börsch-Supan-Nourein iterations as the special cases for $m$=0 and $m$=1, respectively. Some numerical examples are given.  

  • Keywords

Parallel iteration, zeros of polynomial, order of convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-18-283, author = {Zheng , Shi-Ming}, title = {A Family of High-Order Parallel Rootfinders for Polynomials}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {3}, pages = {283--288}, abstract = {

In this paper we present a family of parallel iterations of order $m+2$ with parameter $m=0,1,...$ for simultaneous finding all zeros of a polynomial without evaluation of derivatives, which includes the well known Weierstrass-Durand-Dochev-Kerner and Börsch-Supan-Nourein iterations as the special cases for $m$=0 and $m$=1, respectively. Some numerical examples are given.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9042.html} }
TY - JOUR T1 - A Family of High-Order Parallel Rootfinders for Polynomials AU - Zheng , Shi-Ming JO - Journal of Computational Mathematics VL - 3 SP - 283 EP - 288 PY - 2000 DA - 2000/06 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9042.html KW - Parallel iteration, zeros of polynomial, order of convergence. AB -

In this paper we present a family of parallel iterations of order $m+2$ with parameter $m=0,1,...$ for simultaneous finding all zeros of a polynomial without evaluation of derivatives, which includes the well known Weierstrass-Durand-Dochev-Kerner and Börsch-Supan-Nourein iterations as the special cases for $m$=0 and $m$=1, respectively. Some numerical examples are given.  

Shi-Ming Zheng. (1970). A Family of High-Order Parallel Rootfinders for Polynomials. Journal of Computational Mathematics. 18 (3). 283-288. doi:
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